Canonical forms for mixed symmetric-skewsymmetric quaternion matrix pencils
type: Item
instance of: scholarly article
title: Canonical forms for mixed symmetric-skewsymmetric quaternion matrix pencils
zbMATH Open document ID: 1118.15012
author: Leiba Rodman
published in: Linear Algebra and its Applications
publication date: 2007-06-06T00:00:00Z
review text: The author obtains canonical forms for pairs of quaternionic matrices which are mixed symmetric-skewsymmetric with respect to nonstandard involutory antiautomorphisms of the skew field of real quaternions, under strict equivalence and symmetry respecting congruences. In Section 2 the author recalls basic facts about the quaternionic algebra. Section 3 studies canonical forms for symmetric-skewsymmetric matrix pencils. In Section 4 the author develops some applications of the canonical form of Theorem 3.1. Section 5 presents another application of Theorem 3.1. In Section 6, the author addresses the canonical forms of skewsymmetric quaternionic linear transformations. Section 7 contains the proof of Theorem 3.1.
reviewed by: Yueh-er Kuo
Mathematics Subject Classification ID: 15A21
Mathematics Subject Classification ID: 15B33
Mathematics Subject Classification ID: 15A04
zbMATH DE Number: 5161814
zbMATH Keywords: quaternionic matrices
zbMATH Keywords: involutory antiautomorphisms
zbMATH Keywords: symmetric and skewsymmetric matrices
zbMATH Keywords: canonical forms
zbMATH Keywords: quaternionic algebra
zbMATH Keywords: quaternionic linear transformations
MaRDI profile type: Publication
full work available at URL: j.laa.2006.10.016
OpenAlex ID: W2094581960
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DOI: 10.1016/J.LAA.2006.10.016
description: scientific article; zbMATH DE number 5161814